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Chapter 3
Listing of integrals
3.1
\(\int \tan ^5(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.2
\(\int \tan ^4(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.3
\(\int \tan ^3(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.4
\(\int \tan ^2(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.5
\(\int \tan (d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.6
\(\int \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.7
\(\int \cot (d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.8
\(\int \cot ^2(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.9
\(\int \cot ^3(d+e x) \sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)} \, dx\)
3.10
\(\int \frac{\tan ^5(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.11
\(\int \frac{\tan ^4(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.12
\(\int \frac{\tan ^3(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.13
\(\int \frac{\tan ^2(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.14
\(\int \frac{\tan (d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.15
\(\int \frac{1}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.16
\(\int \frac{\cot (d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.17
\(\int \frac{\cot ^2(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.18
\(\int \frac{\cot ^3(d+e x)}{\sqrt{a+b \tan (d+e x)+c \tan ^2(d+e x)}} \, dx\)
3.19
\(\int \frac{\tan ^7(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.20
\(\int \frac{\tan ^5(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.21
\(\int \frac{\tan ^3(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.22
\(\int \frac{\tan ^2(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.23
\(\int \frac{\tan (d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.24
\(\int \frac{\cot (d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.25
\(\int \frac{\cot ^2(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.26
\(\int \frac{\cot ^3(d+e x)}{(a+b \tan (d+e x)+c \tan ^2(d+e x))^{3/2}} \, dx\)
3.27
\(\int \tan ^5(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.28
\(\int \tan ^3(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.29
\(\int \tan (d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.30
\(\int \cot (d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.31
\(\int \cot ^3(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.32
\(\int \tan ^2(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.33
\(\int \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.34
\(\int \cot ^2(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.35
\(\int \cot ^4(d+e x) \sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx\)
3.36
\(\int \frac{\tan ^5(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.37
\(\int \frac{\tan ^3(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.38
\(\int \frac{\tan (d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.39
\(\int \frac{\cot (d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.40
\(\int \frac{\cot ^3(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.41
\(\int \frac{\tan ^4(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.42
\(\int \frac{\tan ^2(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.43
\(\int \frac{1}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.44
\(\int \frac{\cot ^2(d+e x)}{\sqrt{a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \, dx\)
3.45
\(\int \frac{\tan ^7(d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.46
\(\int \frac{\tan ^5(d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.47
\(\int \frac{\tan ^3(d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.48
\(\int \frac{\tan (d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.49
\(\int \frac{\cot (d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.50
\(\int \frac{\cot ^3(d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
3.51
\(\int \frac{\tan ^2(d+e x)}{(a+b \tan ^2(d+e x)+c \tan ^4(d+e x))^{3/2}} \, dx\)
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